SOLUTION: Assume 3 cos(x) − 4 sin(x) = −3 and 4 cos(x) + 3 sin(x )= 4 Find the exact (numeric) value of cot(x).

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Question 728076: Assume
3 cos(x) − 4 sin(x) = −3
and
4 cos(x) + 3 sin(x )= 4
Find the exact (numeric) value of cot(x).
Answer by lwsshak3(11628) About Me  (Show Source):
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Assume
3 cos(x) − 4 sin(x) = −3
and
4 cos(x) + 3 sin(x )= 4
Find the exact (numeric) value of cot(x).
***
3 cos(x) − 4 sin(x) = −3
4 cos(x) + 3 sin(x )= 4
..
multiply first equation by 4 and second equation by 3
12 cos(x) − 16 sin(x) = −12
12 cos(x) + 9 sin(x )= 12
subtract
12 cos(x) − 16 sin(x) = −12
12 cos(x) + 9 sin(x )= 12
-25sin(x)=-24
sin(x)=24/25=opposite side/hypotenuse
adjacent side=√(25^2-24^2)=√49=7
cot(x)=adjacent side/opposite side=7/24